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A machine gun is mounted on a 2000 kg car on a horizontal frictionless surface. At some instant, the gun fires bullets of mass 10 g with a velocity of 500 m/s with respect to the car. The number of bullets fired per second is ten. The average thrust on the system is:
The value of coefficient of volume expansion of glycerin is $5 \times 10^{-4}\text{ K}^{-1}$. The fractional change in the density of glycerin for a rise of $40^{\circ}\text{C}$ in its temperature is -
The volume ($V$) of a monatomic gas varies with its temperature ($T$), as shown in the graph. The ratio of work done by the gas to the heat absorbed by it when it undergoes a change from state $A$ to state $B$ will be:
In the diagram shown, the normal reaction force between $2 \text{ kg}$ and $1 \text{ kg}$ blocks is: (Consider the surface to be smooth and $g=10 \text{ m/s}^2$)
Given below are two statements: Assertion (A): A standing bus suddenly accelerates. If there was no friction between the feet of a passenger and the floor of the bus, the passenger would move back. Reason (R): In the absence of friction, the floor of the bus would slip forward under the feet of the passenger.
A slab of stone of area of $0.36\text{ m}^2$ and thickness $0.1\text{ m}$ is exposed on the lower surface to steam at $100^{\circ}\text{C}$. A block of ice at $0^{\circ}\text{C}$ rests on the upper surface of the slab. In one hour $4.8\text{ kg}$ of ice is melted. The thermal conductivity of slab is : (Given latent heat of fusion of ice $=3.36 \times 10^5\text{ J kg}^{-1}$)
A Carnot engine has an efficiency of $50\%$ when its source is at a temperature $327^\circ \mathrm{C}$. The temperature of the sink is:
One mole of an ideal diatomic gas undergoes a transition from $A$ to $B$ along a path $AB$ as shown in the figure. The change in internal energy of the gas during the transition is
A point mass $m$ is moved in a vertical circle of radius $r$ with the help of a string. The velocity of the mass is $\sqrt{7gr}$ at the lowest point. The tension in the string at the lowest point is:
A ball of mass 0.15 kg is dropped from a height 10 m, strikes the ground, and rebounds to the same height. The magnitude of impulse imparted to the ball is ($g=10 \text{ m/s}^2$) nearly:
Liquid oxygen at $50\text{ K}$ is heated to $300\text{ K}$ at constant pressure of $1\text{ atm}$. The rate of heating is constant. Which one of the following graphs represents the variation of temperature with time?
A refrigerator works between $4^{\circ}\text{C}$ and $30^{\circ}\text{C}$. It is required to remove $600 \text{ calories}$ of heat every second to keep the temperature of the refrigerated space constant. The power required will be: (Take, $1 \text{ cal} = 4.2 \text{ Joules}$)
For an adiabatic process, the factor which remains constant is: (all the notations have their usual meaning)
When a string is divided into three segments of lengths $l_1, l_2$ and $l_3$, the fundamental frequencies of these three segments are $\nu_1, \nu_2$ and $\nu_3$ respectively. The original fundamental frequency ($\nu$) of the string is:
The potential difference across the 100 Ω resistance in the following circuit is measured by a voltmeter of 900 Ω resistance. The percentage error made in reading the potential difference is:
The measurement of an unknown resistance R is to be carried out using a Wheatstone bridge. Two students perform an experiment in two ways. The first student takes R₂ = 10 Ω and R₁ = 5 Ω. The other student takes R₂ = 1000 Ω and R₁ = 500 Ω. In the standard arm, both take R₃ = 5 Ω. Both find R = (R₂/R₁) × R₃ = 10 Ω within errors. Consider the following statements: (a) The errors of measurement of the two students are the same. (b) Errors of measurement do depend on the accuracy with which R₂ and R₁ can be measured. (c) If the student uses large values of R₂ and R₁, the currents through the arms will be feeble. This will make the determination of the null point accurately more difficult. (d) Wheatstone Bridge is a very accurate instrument and has no errors of measurement. Choose the correct option from the given ones:
Two rods, one made of copper and the other made of steel, of the same length and same cross-sectional area are joined together. The thermal conductivity of copper and steel are $385\text{ J s}^{-1}\text{K}^{-1}\text{m}^{-1}$ and $50\text{ J s}^{-1}\text{K}^{-1}\text{m}^{-1}$ respectively. The free ends of copper and steel are held at $100^{\circ}\text{C}$ and $0^{\circ}\text{C}$ respectively. The temperature at the junction is, nearly:
A mass of diatomic gas ($\gamma=1.4$) at a pressure of $2\text{ atm}$ is compressed adiabatically so that its temperature rises from $27^\circ\text{C}$ to $927^\circ\text{C}$. The pressure of the gas in the final state is:
If $\Delta U$ and $\Delta W$ represent the increase in internal energy and work done by the system respectively in a thermodynamical process, which of the following is true?
Figure shows a potentiometer circuit for comparison of two resistances. The balance point with a standard resistor R = 10.0 Ω is found to be 58.3 cm, while that with the unknown resistance X is 68.5 cm. The value of X is: